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A number of example programs, including

- those with just one or a few rules,
- encodings of various calculi (propositional logic, Petri Nets, lambda calculus, ambient calculus, etc.),
- state-space search using SLIM's nondeterministic execution (typical AI problems etc.),
- model checking (distributed and concurrent algorithms, protocol verification, etc.),
- graph visualization using UNYO-UNYO (fullerenes (C60) etc.),
- those using LMNtal Java's GUI,

and so on, can be found in
**this directory** (click here).

- The
**ltl**subdirectory contains both programs and LTL formulas to model-check them. - The
**unyo**subdirectory contains programs to be run under the UNYO-UNYO visualizer.

All these programs are included in the latest distribution of LaViT.

Let us introduce some simple examples below.

Lists formed with c(cons) and n(il) constructors can be concatenated using the following two rules:

append(X,Y,Z), n(X) :- Y=Z. append(X,Y,Z), c(A,X1,X) :- c(A,Z1,Z), append(X1,Y,Z1).

Enter those rules with the following initial state:

append(c(1,c(2,c(3,n))),c(4,c(5,n)),result).

RESULT: result(c(1,c(2,c(3,c(4,c(5,n)))))) with the two rules above.

The above initial state is written using the *term abbreviation scheme* explained here. By further applying the term abbreviation scheme and the Prolog-like list syntax, the list concatenation program can be written also as:

Z=append([], Y) :- Z=Y. Z=append([A|X1],Y) :- Z=[A|append(X1,Y)]. result = append([1,2,3],[4,5]).

RESULT: result=[1,2,3,4,5] with the two rules above.

Ten agents, each with two free hands, are going to hold hands with others. Is it possible that some agent is left alone?

a(free,free),a(free,free),a(free,free),a(free,free),a(free,free), a(free,free),a(free,free),a(free,free),a(free,free),a(free,free). a(X,free),a(free,Y) :- a(X,C),a(C,Y).

RESULT: Twenty possible final configurations. You can randomly compute them by running the program using LMNtal Java with the **-s** (shuffle) option, or running SLIM with the **-nd** (nondeterministic execution) option. LaViT's **StateViewer** will show you a state transition diagram of the problem.

Two customers with different amounts of coins and hunger are buying chocolates from a vending machine. Each chocolate costs three and only two kinds of coins are considered: one and five.

{customer,a,five,one,one,hunger,hunger}. % Customer a has $7, buying 2 chocolates {customer,b,five,hunger}. % Customer b has $5, buying 1 chocolate {vending,choco,choco,choco,one,one}. % Vending machine has 3 chocolates {customer,$c,hunger,five}, {vending,$v,choco,one,one} :- {customer,$c,choco,one,one}, {vending,$v,five}. {customer,$c,hunger,one,one,one}, {vending,$v,choco} :- {customer,$c,choco}, {vending,$v,one,one,one}.

LaViT with **-nd** will compute two possible final states:

RESULT 1: {customer,a,choco,choco,one}, {customer,b,choco,one,one}, {vending,five,five,one}, <RULES> RESULT 2: {customer,a,hunger,hunger,five,one,one}, {customer,b,choco,one,one}, {vending,choco,choco,five}, <RULES>

Observe that applying each rule preserves the total amount of coins and chocos within the system.